These difficulties were of two kinds; the first arose from the tendency of the round arch, when on a large scale and heavily weighted, to sink at the crown if there is even any very slight settlement of the abutments. If we turn again to diagram 77, and observe the nearly vertical line formed there by the joints of the keystone, and if we suppose the scale of that arch very much increased without increasing the width of each voussoir, and suppose it built in two or three rings one over the other (which is really the constructive method of a Gothic arch), we shall see that these joints in the uppermost portion of the arch must in that case become still more nearly vertical; in other words, the voussoirs almost lose the wedge shape which is necessary to keep them in their places, and a very slight movement or settlement of the abutments is sufficient to make the arch stones lose some of their grip on each other and sink more or less, leaving the arch flat at the crown. There can be no doubt that it was the observance of this partial failure of the round arch (partly owing probably to their own careless way of preparing the foundations for their piers - for the mediaeval builders were very bad engineers in that respect) which induced the builders of the early transitional abbeys, such as Furness and Fountains and Kirkstall, to build the large arches of the nave pointed, though they still retain the circular-headed form for the smaller arches in the same buildings, which were not so constructively important.

This is one of the constructive reasons which led to the adoption of the pointed arch in mediaeval architecture, and one which is easily stated and easily understood. The other influence is one arising out of the lengthened conflict with the practical difficulties of vaulting, and is a rather more complicated matter, which we must now endeavor to follow out.

Figs. 93 107. Figs. 93-107.

Looking at Fig. 92, it will be seen that in addition to the perspective sketch of the intersecting arches, there is drawn under it a plan, which represents the four points of the abutment of the arches (identified in plan and perspective sketch as A, B, C, D), and the lines which are taken by the various arches shown by dotted lines. Looking at the perspective sketch, it will be apparent that the intersection of the two cross vaults produces two intersecting arches, the upper line of which is shown in the perspective sketch (marked e and f); underneath, this intersection of the two arches, which forms a furrow in the upper side of the construction, forms an edge which traverses the space occupied by the plan of the vaulting as two oblique arches, running from A to C and from B to D on the plan. Although these are only lines formed by the intersection of two cross arches, still they make decided arches to the eye, and form prominent lines in the system of vaulting; and in a later period of vaulting they were treated as prominent lines and strongly emphasized by mouldings; but in the Roman and early Romanesque vaults they were simply left as edges, the eye being directed rather to the vaulting surfaces than to the edges. The importance of this distinction between the vaulting surfaces and their meeting edges or groins2 will be seen just now. The edges, nevertheless, as was observed, do form arches, and we have therefore a system of cross arches (A B and C D3 Fig. 95), two wall arches (A, D and B C), and two oblique arches (A C and B D), which divide the space into four equal triangular portions; this kind of vaulting being hence called quadripartite vaulting. In this and the other diagrams of arches on this page, the cross arches are all shown in positive lines, and the oblique arches in dotted lines.

We have here a system in which four semicircular arches of the width of A B are combined with two oblique arches of the width of A C, springing from the same level and supposed to rise to the same height. But if we draw out the lines of these two arches in a comparative elevation, so as to compare their curves together, we at once find we are in a difficulty. The intersection of the two circular arches produces an ellipse with a very flat crown, and very liable to fail. If we attempt to make the oblique arch a segment only of a large circle, as in the dotted line at 94, so as to keep it the same level as the other without being so flat at the top, the crown of the arch is safer, but this can only be done at the cost of getting a queer twist in the line of the oblique arch, as shown at D, Fig. 93. The like result of a twist of the line of the oblique arch would occur if the two sides of the space we are vaulting over were of different lengths, i.e., if the vaulting space were otherwise than a square, as long as we are using circular arches. If we attempt to make the oblique arches complete circles, as at Fig. 96, we see that they must necessarily rise higher than the cross and side arches, so that the roof would be in a succession of domical forms, as at Fig. 97. There is the further expedient of "stilting" the cross arches, that is, making the real arch spring from a point above the impost and building the lower portion of it vertical, as shown in Fig. 98. This device of stilting the smaller arches to raise their crowns to the level of those of the larger arches was in constant use in Byzantine and early Romanesque architecture, in the kind of manner shown in the sketch, Fig. 99; and a very clumsy and makeshift method of dealing with the problem it is; but something of the kind was inevitable as long as nothing but the round arch was available for covering contiguous spaces of different widths. The whole of these difficulties were approximately got over in theory, and almost entirely in practice, by the adoption of the pointed arch.

By its means, as will be seen in Fig. 100, arches over spaces of different widths could be carried to the same height, yet with little difference in their curves at the springing, and without the necessity of employing a dangerously flat elliptical form in the oblique arch. A sketch of the Gothic vault in this form, and as the intersection of the surfaces of pointed vaults, is shown in Fig. 101.